Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810680 | C2 | semidirect |
| 3. #16810352 | C2 | semidirect |
| 4. C4×M16×C53 | C2 | semidirect |
| 13. C4⋊#88322 | C22 | semidirect |
| 19. C4×C8×C53 | C22 | semidirect |
| 60. D212 | M16 | semidirect |
| 88. C4×M16 | D53 | semidirect |
| 90. C53 | #1490 | semidirect |
| 105. C4×C8 | C2×D53 | semidirect |